Question

how to graph general rational functions?
like y=2x/x^2-1

Answer 1

\[y=\frac{2x}{x^2-1}\]
\[y=\frac{2x}{(x-1)(x+1)}\]

the function will be zero at x=0
so there will be asymptotes at \[x=\pm1\]

Answer 2

when \(0<< x\) (x is a large positive number)

the numerator will be large and positive, but the denominator much larger and will dominate, and hence the function will be small

when \(x<<0\) (x is large negative number)

the numerator will be negative and large, but the denominator will again dominate and hence the function will be small and negative

Answer 3

so*and